 | United States Military Academy - 1942 - 1028 pages
...between the areas of a circumscribed equilateral triangle and an inscribed regular hexagon. 16 Prove that the sum of the squares of two sides of a triangle is equal to twice the square of half the third side, plus twice the square of the median to the third side. 10 Construct the common external... | |
 | Ross Honsberger - Mathematics - 1996 - 276 pages
...already reached the crucial relation, for it remains only to think of the quite well-known theorem that the sum of the squares of two sides of a triangle is equal to twice the square on the median to the third side plus one-half the square on the third side: XY2 + XZ2 = 2XW2 + YZ2.... | |
 | Ross Honsberger - Mathematics - 1997 - 332 pages
...and BD be X and Y and the midpoint of XY be Z (figure 192). Our solution is based on the theorem that the sum of the squares of two sides of a triangle is equal to twice the square of the FIGURE 192 FIGURE 193 median to the third side increased by one-half the square of the third side.... | |
 | Mathematics - 1904 - 1000 pages
...and conversely," should be omitted. It does not relate to any subsequent proposition. I would omit, "The sum of the squares of two sides of a triangle is equal to twice the square of half the third side, etc. ; the difference of the squares, etc. ; the square of the bisector of an angle of... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 356 pages
...of the circumscribed and inscribed circles. EXERCISES THEOREMS AND Locus PROBLEMS 1. The difference of the squares of two sides of a triangle is equal to the difference of the squares of the segments made by the altitude upon the third side. 2. The sum... | |
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The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side. 
